arXiv subjects

Bastian Castorene

Publications and source records attributed to Bastian Castorene.

10 recordsLinked to original sources

arXiv2026

Equilibrium Thermodynamics of Non-Hermitian Dirac Fermions: Caloric and Magnetic Responses

We establish scaling relations governing the equilibrium thermodynamics of real-spectrum non-Hermitian Dirac fermions in a magnetic field. Assuming thermalization with respect to the quasi-Hermitian Hamiltonian, a similarity transformation maps the system at the same applied field onto a Hermitian Dirac model with reduced velocity, while the Landau-level spectrum also admits a representation in terms of a reduced effective magnetic field. This structure yields scaling relations for the chemical potential, entropy, heat capacities, and orbital magnetic response in different thermodynamic ensembles. At fixed projected filling factor (PFF), the self-consistent chemical potential follows the compressed ladder of Landau levels, and the canonical thermodynamic functions are rescaled Hermitian responses. At fixed chemical potential, Landau-level crossings generate oscillatory caloric and magnetic responses governed by the same spectral compression. Quasistatic non-Hermitian deformation at fixed PFF further yields adiabatic temperature scaling. More broadly, these results establish a thermodynamic framework for real-spectrum non-Hermitian quantum matter and provide a starting point for incorporating the effects of interactions and disorder within the same formalism.

quant-ph↗

arXiv2026

Caloric Phenomena and Stirling-Cycle Performance in Heisenberg- Kitaev Magnon Systems

We investigate the Stirling-cycle performance of a Heisenberg--Kitaev magnonic medium with Dzyaloshinskii--Moriya (DM) interactions. Using linear spin-wave theory, we show the DM interaction preserves spectral symmetry, yielding even caloric responses and symmetric Stirling engine efficiency. In contrast, bond-dependent Kitaev exchange asymmetrically distorts the magnonic density of states, enabling distinct direct and inverse caloric effects. Consequently, Kitaev-driven cycles achieve significantly higher efficiencies than DM-driven protocols, approaching a high-performance saturation regime for negative couplings. This establishes exchange-anisotropic magnets as highly tunable platforms for nanoscale solid-state energy conversion.

cond-mat.stat-mech↗

arXiv2026

Thermal Hofstadter Butterflies

Fractal electronic spectra arising from the competition between lattice periodicity and magnetic flux are a fundamental hallmark of two-dimensional quantum systems. While the spectral properties of Hofstadter butterflies are well documented, their thermodynamic response has remained remarkably unexplored. We present an original characterization of the electronic entropy $S_{e}$, and specific heat $C_{e}$, at half-filling, for square, honeycomb, and triangular lattices under a magnetic field. We demonstrate that these observables exhibit fast and slow magneto-thermo oscillations and pronounced magnetocaloric effects. We identify striking self-similarity in $S_e$ and $C_e$, tracing heart-shaped specific heat and tunnel-like entropy contours that repeat at specific lattice-dependent magnetic fluxes. Entropy minima at low temperatures play a remarkable role, acting as fingerprints for the butterfly spines, resolving the underlying fractal spectra. These findings may establish thermal measurements as high-resolution spectroscopic probes, providing a robust framework for recognizing fractal signatures through thermodynamics in diverse nanostructures.

cond-mat.mes-hall↗

arXiv2025

Exact Combinatorial Density of States for the Critical 1D Ising Model

This work presents an exact microcanonical combinatorial analysis of the one-dimensional antiferromagnetic Ising model. At the primary ground-state level crossing $B/J=2$, degeneracies follow the Fibonacci and Lucas sequences for open chains and periodic rings, respectively. We extend this framework to the complete excitation spectrum, demonstrating that the density of states is constructed from topological defects governed by linear Diophantine equations and $p$-fold Fibonacci convolutions. Open boundaries act as fractional defects, densifying the chain spectrum into energy steps of $2J$, whereas the closed ring remains quantized in units of $4J$. Notably, this exact topological counting exposes non-trivial spectral gaps near the fully polarized limit, strictly forbidding the penultimate macroscopic energy levels in both topologies. Through the transfer matrix formalism, we derive exact closed-form expressions for the critical degeneracies at all energy levels. These results provide a rigorous analytical foundation for extracting exact residual entropies and exposing the intrinsic number-theoretic architecture of quantum critical manifolds.

cond-mat.stat-mech↗

arXiv2025

Fundamental Work Scaling and Non-Extensivity in Critical Engines

We present a general analytical framework for critical two-isothermal engines that emerge operationally from quasi-static quantum Stirling cycles across ground-state level crossings (GLCs) in the low-temperature regime, where reversible heat exchange is governed by the structural entropy change while the internal energy remains constant. Within this ideal-reservoir, low-temperature equilibrium model, the Primarch Formula gives an exact quasistatic ensemble-average expression linking extracted work and efficiency directly to macroscopic ground-state degeneracies. In this reversible setting, the engines reach Carnot efficiency without a classical regenerator. For the perturbative population pattern analyzed here, thermal excitations reduce the ideal work and efficiency. Validated against exact numerical simulations of generalized \textit{N}-th spin-s Heisenberg models with nontrivial interactions, the framework is applied to the one-dimensional antiferromagnetic Ising model, revealing a profound connection to number theory. Governed by Fibonacci-Lucas and parity-dependent critical degeneracies, the engine exhibits three distinct work-scaling regimes: persistent logarithmic non-extensivity, recovery of extensivity in the thermodynamic limit, and asymptotic extensivity with a logarithmic finite-size correction. In all three regimes, Carnot efficiency is attained within the reversible equilibrium model.

cond-mat.stat-mech↗

arXiv2025

Reaching maximum efficiency in quantum Stirling engines using multilayer graphene

In this work, quantum Stirling engines based on monolayer, AB-stacked bilayer, and ABC-stacked trilayer graphene under perpendicular magnetic fields are analyzed. Performance maps of the useful work $(\eta W)$ reveal a robust optimum at low magnetic fields and moderately low temperatures, with all stackings capable of reaching Carnot efficiency under suitable configurations. The AB bilayer achieves this across the broadest parameter window while sustaining finite work, the monolayer exhibits highly constrained regimes, and the trilayer shows smoother trends with sizable $\eta W$. These results identify multilayer graphene, particularly the AB bilayer, as a promising platform for efficient Stirling engines, while also highlighting the versatility of the monolayer in realizing all four operational regimes of the Stirling cycle.

cond-mat.stat-mech↗

arXiv2025

Entropy-Seebeck ratio as a tool for elementary charge determination

In this work, we investigate the relationship between the Seebeck coefficient $(S)$, and the differential entropy per particle (DEP, $s$), as a tool for characterizing charge carriers in two-dimensional systems. Using armchair silicene nanoribbons as a model platform, we analyze how both quantities and their ratio depend on chemical potential at room temperature. While the Seebeck coefficient captures transport properties through the energy dependence of the electronic transmission, the DEP is directly connected to the system's electronic entropy, offering a direct thermodynamic alternative for estimating $S$. We evaluate these transport-thermodynamic properties considering diverse ribbon widths, defining metallic and semiconducting regimes. We find both quantities $S$ and $s$, are highly interconnected within the ribbon's band gap energy region, and their ratio $s/S$ converges to the elementary charge $e$ across that energy window, fulfilling the Kelvin formula $S=s/e$. On the contrary, $s/S$ is undefined for gapless ribbons in the energy window of the first transmission channel. These results establish the ratio between the DEP and the Seebeck coefficient as a reliable and complementary probe for the determination of the elementary charge, and to identify the cleanness of electronic band gaps as $s/S$ matches with $e$.

cond-mat.mes-hall↗

arXiv2025

Quantum Level-Crossing Induced by Anisotropy in Spin-1 Heisenberg Dimers: Applications to Quantum Stirling Engines

This work explores the thermodynamic performance of a quantum Stirling heat engine implemented with an anisotropic spin-1 Heisenberg dimer as the working medium. Using the Hamiltonian of the system, we analyze the interplay of anisotropy, magnetic field, and exchange interactions and their influence on the energy spectrum and the quantum level crossing. Our results reveal that double-degenerate point (DDP) and a triple-degenerate point (TDP) play pivotal roles in shaping the operational regimes and efficiency of the quantum Stirling engine. At those points, the Carnot efficiency reaches higher work output and enhanced stability, making it a robust candidate for optimal thermodynamic performance. These findings highlight the potential of anisotropic spin systems as viable platforms for quantum heat engines and contribute to advancing the field of quantum thermodynamics.

cond-mat.stat-mech↗

arXiv2025

Entropy, entanglement and susceptibility of three qubits near quantum criticality

This work investigates a system of three entangled qubits within the XXX model, subjected to an external magnetic field in the $z$-direction and incorporating an anisotropy term along the $y$-axis. We explore the thermodynamics of the system by calculating its magnetic susceptibility and analyzing how this quantity encodes information about entanglement. By deriving rigorous bounds for susceptibility, we demonstrate that their violation serves as an entanglement witness. Our results show that anisotropy enhances entanglement, extending the temperature range over which it persists. Additionally, by tracing over the degrees of freedom of two qubits, we examine the reduced density matrix of the remaining qubits and find that its entropy under the influence of the magnetic field can be mapped to an effective thermal bath at $(B,K) > 0$ K.

cond-mat.stat-mech↗

arXiv2024

Effects of Magnetic Anisotropy on 3-Qubit Antiferromagnetic Thermal Machines

This study investigates the anisotropic effects on a system of three qubits with chain and ring topology, described by the antiferromagnetic Heisenberg XXX model subjected to a homogeneous magnetic field. We explore the Stirling and Otto cycles and find that easy-axis anisotropy significantly enhances engine efficiency across all cases. At low temperatures, the ring configuration outperforms the chain on both work and efficiency during the Stirling cycle. Additionally, in both topologies, the Stirling cycle achieves Carnot efficiency with finite work at quantum critical points. In contrast, the quasistatic Otto engine also reaches Carnot efficiency at these points but yields no useful work. Notably, the Stirling cycle exhibits all thermal operational regimes engine, refrigerator, heater, and accelerator unlike the quasistatic Otto cycle, which functions only as an engine or refrigerator.

cond-mat.stat-mech↗